Question

prove that in parallogram ,opposite angle are equal​

Answer 1

Proof:

Given: ABCD is a parallelogram.

To Prove: The opposite sides are equal, AB = CD and BC = AD.

In parallelogram ABCD, compare triangles ABC and CDA. In these triangles:

AC = CA (common side)∠BAC = ∠DCA (alternate interior angles)∠BCA = ∠DAC (alternate interior angles)

Hence by the ASA criterion, both the triangles are congruent and the corresponding sides are equal. Therefore we have AB = CD, and BC = AD.

Answer 2

Answer:

Here, ABCD is a parallelogram with AC as its diagonal.

We know, in parallelogram opposites sides are parallel.

So, AB∥DC and AD∥BC

Since, AB∥DC and AC is the transversal

⇒ ∠BAC=∠DCA ---- ( 1 ) [ Alternate angles ]

Similarly, AD∥BC and AC is the transversal.

⇒ ∠DAC=∠BCA ---- ( 2 ) [ Alternate angles ]

Adding ( 1 ) and ( 2 ),

⇒ ∠BAC+∠DAC=∠DCA+∠BCA

⇒ ∠BAD=∠DCB

Similarly, we can prove, ∠ADC=∠ABC

∴ We have proved that, opposite angles of a parallelogram are equal.

Step-by-step explanation:

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